{"paper":{"title":"$Q$-polynomial distance-regular graphs and a double affine Hecke algebra of rank one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.RT","authors_text":"Jae-Ho Lee","submitted_at":"2013-07-19T18:04:09Z","abstract_excerpt":"We study a relationship between $Q$-polynomial distance-regular graphs and the double affine Hecke algebra of type $(C^{\\vee}_1,C_1)$. Let $\\Gamma$ denote a $Q$-polynomial distance-regular graph with vertex set $X$. We assume that $\\Gamma$ has $q$-Racah type and contains a Delsarte clique $C$. Fix a vertex $x \\in C$. We partition $X$ according to the path-length distance to both $x$ and $C$. This is an equitable partition. For each cell in this partition, consider the corresponding characteristic vector. These characteristic vectors form a basis for a $\\mathbb{C}$-vector space ${\\bf W}$.\n  The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5297","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}